Math History Tidbits: Agnesi, Euler, and China

I’ve fallen behind on my project of transcribing my Alexandria Jones stories. Finally, here are a few more tidbits from math history, along with links to relevant Internet sites and a few math puzzles for your students to try.

I hope you find them interesting.

Math in the Trinity

Since these historical tidbits were published in the December edition of my old math newsletter, I included a short Bible verse for Christmas:

Being in very nature God, He did not consider equality with God something to be grasped, but made Himself nothing…

Maria Agnesi

Alexandria Jones’s mother, Maria, is named for Maria Gaetana Agnesi (1718-1799). Maria was one of the first women to be accepted as a serious mathematician.

Maria Agnesi was both beautiful and a genius. As a child she mastered French, German, Greek, Hebrew, Latin, and Spanish — as well as her native Italian.

On at least one occasion, Maria worked mathematics while sleepwalking. When she got stumped, she left the problem on her desk and went to bed. The next morning, she found the correct solution neatly written on her paper.

After teaching calculus to her younger brothers, Agnesi wrote what became Europe’s most popular calculus textbook for the next 50 years.

It took much skill and sagacity to reduce, as the author has done, to almost uniform methods these discoveries scattered among the works of modern mathematicians and often presented by methods very different from each other. Order, clarity and precision reign in all parts of this work. … We regard it as the most complete and best made treatise.

Included in her textbook was a discussion of the curve which, because of another writer’s typographical mistake, has come to be called the Witch of Agnesi.

But there was something Maria loved more than math — she longed to become a nun, but her father forbid it. After her father died, she turned their house into a hospice and spent her fortune helping the poor and infirm. She died in poverty, a patient in that same institution.

The Great Leonhard Euler

Alex’s little brother is named for Leonhard Euler (pronounced OIL-er), who had humility and a sense of humor, as shown in the above quote. But most of all, he had a creative way with numbers. In fact, Leonhard Euler changed the face of math for all time. In addition to several bookshelves full of new work, he revised almost all the math that had been done before his time. Among other things, Euler gave us the symbol , e for natural logarithms, i for imaginary numbers, and for summation.

Euler first learned mathematics from his father, a protestant minister who had studied under Jacob Bernoulli. When Leonhard entered the University of Basel at age 14:

… I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. … True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand …

Understanding of this question is to be sought in the word “sum”; this idea, if thus conceived — namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken — has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.

In the old days, Chinese people called the Yellow River valley “Middle Kingdom” — the center of the world. According to legend, the Emperor Yu (c. 2200 BC) was traveling the Yellow River [or perhaps the Lo River, see this comment] one day when he spotted the divine tortoise Lo-shu on the bank. Lo-shu’s back was decorated with a magic square, which Emperor Yu adopted as a good-luck charm.

Tidbits

For awhile, the symbol p was used to stand for the circumference of a circle. In 1706, an Englishman named William Jones used as we do today — to stand for the ratio of the circumference to the circle’s diameter. Few people picked up on that idea, however, until Leonhard Euler decided to use in 1737.

Almost 1500 years ago, the Chinese writer Tsu Ch’ung-chih estimated to be about equal to 355/113. How close was he?

Post navigation

5 thoughts on “Math History Tidbits: Agnesi, Euler, and China”

I’m curious about your comment that Maria Gaetana Agnesi was “both beautiful and a genius.” I have been researching Agnesi, and the only primary source I can find describing her appearance said she was “neither ugly nor pretty.” Do you have a source that called her “beautiful”?

I don’t remember what my sources said, since this was originally published years ago and my notes have been misplaced in several moves. That may have been my own opinion, based on the painting of her as a young woman — but of course, paintings can be fudged.

Browse the Blog Posts by Category

Fantasy Adventures by a Homeschooled Teen Novelist

Privacy Notice

If you want to comment on a post, we ask for your name (you can use a pseudonym) and email address‌—‌your home website is optional, for those who want the link. This helps us detect and avoid spam comments.

If you subscribe to blog posts by email (the blue envelope icon in the social media links above), those come from Feedburner, which is a Google service. You can read Google’s privacy policy here.

If you ask to receive updates about our books, we use your email address only to send you the newsletter(s) you request. These updates will include promotional material such as notice of a book release, limited-time discount prices, or other news.

We will not contact you directly unless it’s necessary to reply to your comment or question. For instance, if you offered to host the Playful Math Education Blog Carnival, we’ll need to confirm your date and send you information. We LOVE carnival hosts!

We do not share your name or email, except where it’s necessary to provide the service (comment posting or newletter) you requested, or unless the law requires us to do so.

Affiliate Disclosure

Almost all of the book covers featured on this site link to Amazon.com‌—‌either directly or through a service called Skimlinks‌—‌where you can read descriptions and reviews, and where I earn a small commission if you actually buy a book. But if you have access to a good library loan system, you should be able to read most of the books for free.Amazon.com Privacy PolicySkimlinks Privacy Policy